I have a few questions about finding equations and such for parabolas

I attempted both of these problems and would like some help finishing, or re-doing them if needed.

Find the vertex of the parabola y=2x^2-12x+23.

My Work:

y= 2x(x-6)+23

(y-23)=2x(x-6)

Am I on the right track here? I know its not done, but I don't know how to go from here assuming I did it right to begin with.

2nd problem:

Write the equation of the parabola with focus (3,4) and directrix x=1.

For the vertex I got (2,4)

So the equation so far is (x-2)^2=4P(y-4)

Help from here getting P would be great also assuming I've done the work correctly...

Thanks a bunch!